Nonstationary flow surface theory for modeling the viscoplastic behaviors of soils

This paper presents a three-dimensional elastic viscoplastic model that can describe the time-dependent behaviors of soft clays. The constitutive model is formulated based on the nonstationary flow surface theory and incorporates new developments, including (i) an improved definition of the nonstationary flow surface that is capable of capturing the stress–strain behaviors under different loading paths, (ii) a unique stress–strain—viscoplastic-strain-rate equation that is able to explicitly describe the nonstationary flow surface, and (iii) a final stable state concept that identifies the final equilibrium state at the end of creep and stress relaxation, which is also used to simplify the loading criteria. The consistency condition is validated for the proposed model, and the viscoplastic multipliers are calculated by solving the consistency equations. The model performance is investigated and validated via simulation of both oedometer and triaxial tests. The numerical results demonstrate that the proposed model is able to reproduce the main viscoplastic behaviors of soils, including creep, undrained creep rupture, stress relaxation, rate effect and accumulated effect.